from manim import *



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
         # 第一个文本对象
        text = Tex(r"$\text{设函数 } f(x) \text{ 在 } x=0 \text{ 处二阶可导且 } \lim\limits _{x\rightarrow 0}\dfrac{f\left( x\right) }{x^{3}}=1\text{ ,则}$",
                   tex_template=TexTemplateLibrary.ctex).scale(5).move_to([-10, 0, 0])

        # 第二个文本对象
        #text0 = Tex(r"$\text{下述论断正确的是()}$",
                    #tex_template=TexTemplateLibrary.ctex).scale(5).next_to(text, RIGHT, buff=1)

        # 第三个文本对象
        text1 = Tex(r"$(A)\lim\limits _{x\rightarrow 0}\dfrac{f'\left( x\right) }{x^{2}}=3$",
                    tex_template=TexTemplateLibrary.ctex).scale(5).move_to([-32, -5, 0])
        text2 = Tex(
                    r"$(B)f''\left( 0\right) =0$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([12,-5,0])
        text3 = Tex(
                   r"$(C)\lim\limits _{x\rightarrow 0}\dfrac{f''\left( x\right) }{x}=6$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-32,-12,0])
        text4 = Tex(
                    r"$(D)f'''\left( 0\right) =6$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([12,-12,0])

        self.play(Write(text),self.camera.frame.animate.scale(0.8),Write(text1),Write(text2),Write(text3),Write(text4))
        self.wait(0.1)
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        self.play(text.animate().move_to([-10,20,0]),text1.animate().move_to([-32,15,0]) ,text2.animate().move_to([12,15,0]),text3.animate().move_to([-32,8,0]),text4.animate().move_to([12,8,0]) )
        self.wait(0.1)
         #半透明矩阵扩展
        rectangle=Rectangle(color=YELLOW,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-32,15,0])
        rectangle0=Rectangle(color=YELLOW,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-32,8,0])
        self.play(
            rectangle.animate.stretch(23.0,dim=0)
            ,rectangle0.animate.stretch(23.0,dim=0)
        )
        self.wait(0.1)

        text5 = Tex(
                   r"$1=\lim\limits _{x\rightarrow 0}\dfrac{f\left( x\right) }{x^{3}}===\lim\limits _{x\rightarrow 0}\dfrac{f'\left( x\right) }{3x^{2}}===\lim\limits _{x\rightarrow 0}\dfrac{f''\left( x\right) }{6x}$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-5,0])
        self.play(Create(text5))
        self.wait(0.1)
        text6 = Tex(
                   r"\text{洛}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,-2,0])
        text60 = Tex(
                   r"\text{洛}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([3,-2,0])
        self.play(Create(text60),Create(text6))
        self.wait(0.1)

        #两个问号

        text61 = Tex(
                   r"\text{?}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-17,2,0])
        text62 = Tex(
                   r"\text{?}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([3,2,0])
        self.play(Create(text61),Create(text62))
        


        #洛必达三个条件

        text8 = Tex(
                   r"}$1.\dfrac{0}{0}$\text{型}"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,-15,0])
        text9 = Tex(
                    r"\text{2.去心领域可导} "
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,-20,0])
        text10 = Tex(
                   r"\text{3.洛后极限三种情况：存在,∞,震荡}"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,-25,0])

        self.play(Create(text8),Create(text9),Create(text10))
        self.wait(0.1)

        rectangle2=Rectangle(color=BLUE,fill_opacity=0.0,width=45,height=11.5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle2.move_to([-22, -17, 0])
        self.play(Create(rectangle2))
        self.wait(0.1)

        text11 = Tex(
                   r"\text{存在性}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([10,-17,0])
        self.play(Create(text11))
        self.wait(0.1)
        rectangle3=Rectangle(color=BLUE,fill_opacity=0.0,width=45,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle3.move_to([-22, -25, 0])
        self.play(Create(rectangle3))
        self.wait(0.1)

        text12 = Tex(
                   r"\text{有用性}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([10,-25,0])
        self.play(Create(text12))
        self.wait(0.1)

         #框框
        rectangle1=Rectangle(color=BLUE,fill_opacity=0.0,width=16.5,height=5.5
                            ,stroke_color=RED,stroke_width=20)
        rectangle1.move_to([-30, -5, 0])
        self.play(Create(rectangle1))
         #半透明矩阵扩展
        rectangle4=Rectangle(color=GREEN,fill_opacity=0.5,width=1,height=5
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,-15,0])
        self.play(
            rectangle4.animate.stretch(45.0,dim=0)
        )
        self.wait(0.1)

        rectangle5=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=5
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,20,0])
        self.play(
            rectangle5.animate.stretch(35.0,dim=0)
        )
        self.wait(0.1)
        text13 = Tex(
                   r"\text{则有}$f'(x) \text{ 在 } x=0 \text{领域连续} $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,25,0])
        self.play(Create(text13))
        self.wait(0.1)
        #半透明框框下移

        self.play(
           
            rectangle4.animate.move_to([-22,-20,0])
        )

        #框框移动
        self.play(
            FadeOut(rectangle5),
            FadeOut(text13),
            FadeOut(text61),
            rectangle1.animate.shift(20*RIGHT),
            FadeOut(rectangle4)

        )
        rectangle5=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=5
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,20,0])
        self.play(
            rectangle5.animate.stretch(35.0,dim=0)
        )
        self.wait(0.1)
        text13 = Tex(
                   r"\text{则有}$f'(x) \text{ 在 } x=0 \text{领域连续} $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,25,0])
        self.play(Create(text13))
        self.wait(0.1)

        self.play(
            FadeOut(rectangle5),
            FadeOut(text13)
        )
        self.wait(0.1)

        text14 = Tex(
                   r"$\infty $",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10, 0, 0])
        self.play(Create(text14))
        self.wait(0.1)

        #透明框框扩展

        rectangle6=Rectangle(color=GREEN,fill_opacity=0.5,width=1,height=5
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,-25,0])
        self.play(
            rectangle6.animate.stretch(45.0,dim=0)
        )
        self.wait(0.1)

        #曲线箭头

        #曲线箭头
        # 创建一个带有箭头的曲线，让箭头向上凸
        curved_arrow = CurvedArrow(
            start_point=[-15, 0, 0],  # 起始点坐标
            end_point=[-25, 0, 0],  # 终止点坐标
            angle=PI/4,  # 弯曲的弧度，向上凸
            tip_shape=StealthTip,  # 箭头类型
            color=BLUE,
            stroke_width=20 
        )
         # 缩放箭头头部
        curved_arrow.tip.scale(3)
        
        # 添加到场景中并播放动画
        self.play(Create(curved_arrow))
        self.wait(0.1)
        self.play(
            FadeOut(curved_arrow),
            FadeOut(text14),
            
        )
        self.wait(0.1)

        #半透明框框上移
        self.play(
           
            rectangle6.animate.move_to([-22,-15,0])
        )
        #题目条件
        rectangle5=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=5
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,20,0])
        self.play(
            rectangle5.animate.stretch(35.0,dim=0)
        )
        self.wait(0.1)
        text13 = Tex(
                   r"\text{则有}$f'(x) \text{ 在 } x=0 \text{可导} $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,25,0])
        self.play(Create(text13))
        self.wait(0.1)
        #半透明框框下移+变红
        self.play(
           
            rectangle6.animate.move_to([-22,-20,0]).set_color(RED)
        )
        self.wait(0.1)
        
        self.play(
            FadeOut(rectangle5),
            FadeOut(text13)
        )
        self.wait(0.1)

        text13 = Tex(
                   r"\text{修改：}$f(x) \text{ 在 } x=0 \text{领域内二阶可导} $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,25,0])
        self.play(Create(text13))
        self.wait(0.1)

        #半透明框框变绿
        self.play(
           
            rectangle6.animate.move_to([-22,-20,0]).set_color(GREEN)
        )
        self.wait(0.1)

        #框框移动到第三个极限
        self.play(
            FadeOut(text62),
            rectangle1.animate.shift(20*RIGHT),
            FadeOut(rectangle6)
        )

        text14 = Tex(
                   r"\text{修改：}$f(x) \text{ 在 } x=0 \text{三阶可导} $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-17,25,0])

        #文本丝滑变化
        self.play(
            ReplacementTransform(text13,text14)
        )
        self.wait(0.5)

        text15 = Tex(
                   r"$=\dfrac{f'''\left( 0\right) }{6}$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([25,-5,0])
        text16 = Tex(
                   r"\text{存在}",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([35,-5,0])
        self.play(Create(text15))
        self.play(Create(text16))
        self.wait(0.1)
        #长框框

        rectangle5=Rectangle(color=BLUE,fill_opacity=0.0,width=80,height=10
                            ,stroke_color=YELLOW,stroke_width=20)
        rectangle5.move_to([0, -5, 0])
        self.play(Create(rectangle5))

        #清空部分元素
        self.play(Uncreate(text16),FadeOut(text15),FadeOut(rectangle0),FadeOut(rectangle)
                  ,Uncreate(text6),FadeOut(rectangle1),FadeOut(rectangle5)
                  ,Uncreate(text60),Uncreate(text5),Uncreate(text14)
                  ,FadeOut(rectangle2),FadeOut(rectangle3),Uncreate(text11),Uncreate(text12)
                  ,Uncreate(text8),Uncreate(text9),Uncreate(text10))
        
        #分析BD

        #半透明矩阵扩展
        rectangle=Rectangle(color=YELLOW,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([12,15,0])
        rectangle0=Rectangle(color=YELLOW,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([12,8,0])
        self.play(
            rectangle.animate.stretch(23.0,dim=0)
            ,rectangle0.animate.stretch(23.0,dim=0)
        )
        self.wait(0.1)


        #箭头引出
        arrow = Arrow(start=[0,25,0],end=[-5,23,0], color=RED
                       , stroke_width=20, tip_length=1)
        self.play(Create(arrow))

        #D选项框框淡出
        self.play(
            FadeOut(rectangle0),
            FadeOut(arrow)
        )
        self.wait(0.1)

        #框框标记
        rectangle1=Rectangle(color=BLUE,fill_opacity=0.0,width=15,height=7
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle1.move_to([7.5, 20, 0])
        self.play(Create(rectangle1))
        #箭头引出+文本
        arrow2 = Arrow(start=[15,23,0],end=[22,23,0],color=RED
                       , stroke_width=20, tip_length=1)

        self.play(GrowArrow(arrow2))
        text17 = Tex(
                   r"$\lim\limits _{x\rightarrow 0}\dfrac{f\left( x\right) }{x^{2}}=0$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([35,23,0])
        self.play(Create(text17))


        text18 = Tex(
                   r"$\lim\limits _{x\rightarrow 0}\dfrac{f\left( 0\right) +f'\left( 0\right) x+\dfrac{f''\left( 0\right) }{2}x^{2}+o\left( x\right) ^{2}}{x^{2}}=0$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-5,0])
        self.play(Create(text18))

        text19 = Tex(
                   r"$0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-16,3,0])
        self.play(Create(text19))
        text20 = Tex(
                   r"$0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-7.5,3,0])
        self.play(Create(text20))

        text20 = Tex(
                   r"$0$",color=PURE_GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([3,3,0])
        self.play(Create(text20))































        self.wait()
